Sheng-Guo Wang

Robust Control for Structural Systems with Parametric and Unstructured Uncertainties

Tall, slender structures and long bridges inherit numerous uncertainties due to model errors, stress calculations, material properties, and load environments and may undergo large forces from natural hazards such as earthquakes and strong wind events. This paper develops a robust active control approach with para metric uncertainty in the system and control input and unstructured uncertainty in the disturbance input ma trices based on an uncertain structural system. A special single-valued decomposition (SVD) is applied to structured uncertain structures. The robust control law provides robust relative stability, an H ∞-norm distur bance attenuation, and H 2 optimality. The H ∞ norm of the transfer function from the external disturbance forces (e.g., earthquake, wind, etc.) to the observed system states is restricted by a prescribed attenuation in dex δ. Preservation of robust H 2 optimality of uncertain structural systems is discussed. This paper considers both structured uncertainties and norm-bounded unstructured uncertainties. Numerical simulations that use the robust controller show significant reduction in vibrations.

Robust optimal pole-placement in a vertical strip and disturbance rejection

Abstract This paper presents a linear quadratic regulator (LQR) for robust closed-loop pole-placement within a vertical strip, and disturbance rejection with an H ∞-norm constraint for the uncertain linear systems. The concerned systems cover both matched and mismatched uncertain linear systems with unstructured or structured uncertainties existing in both the system and input matrices. A set of tuning parameters is incorporated for some flexibility in finding a solution to the algebraic Riccati equation, and a controller gain parameter is selected for robust pole clustering. Also, a constraint is established to verify whether the proposed robust LQRs preserve H 2 optimality with respect to a specific quadratic cost function.

Efficient local AADT estimation via SCAD variable selection based on regression models

In transportation networks, Annual Average Daily Traffic (AADT) estimation is very important to decision making, planning, air quality analysis, etc. Regression method may be the most popular one for estimating AADT on non-counters roads. Most literatures focus on how to collect different groups of predicting variables, and select significant variables by t-test and F-test. However, there is no theory on the validity of these multiple selecting steps. Furthermore, variables they collected for high functional class roads may be not suitable for the estimation of local AADT because of lacking counters. This paper focuses on the estimation and variable selection for the local AADT using different groups of variables. The variable selection by smoothly clipped absolute deviation penalty (SCAD) procedure is proposed. It can select significant variables and estimate unknown regression coefficients simultaneously at one step. The estimation algorithm and the tuning parameters selection are presented. The used data is from Mecklenburg County of North Carolina in 2007 for demonstration. The proposed method shows that our selection procedure is valid and it further improves the local AADT estimation by incorporating satellite information. The proposed method outperforms some other regression method when it is applied to local AADT estimation.

Worst case analysis of linear analog circuit performance based on Kharitonov's rectangle

In the spirit of Kharitonovs rectangle, an efficient worst case analysis approach for linear analog circuit performance under process variations is proposed in this paper. By contrast with the Monte Carlo method, the proposed approach strongly reduces the computation to only evaluate a few of Kharitonov-type critical transfer functions, whose envelop will give the worst case variation range of performance metrics. The computational efficiency of the method suggested is demonstrated by a real analog circuit example.

Robust control for structural systems with parametric and unstructured uncertainties

Tall, slender structures and long bridges that inherit numerous uncertainties due to model errors, stress calculations, material properties, and load environments, may undergo large forces from natural hazards such as earthquakes and strong wind events. The paper develops a robust active control approach with parametric uncertainties in the system and control input, and unstructured uncertainties in disturbance input matrices based on an uncertain structural system. Special single valued decomposition (SVD) is applied to structured uncertain structures. The robust control law provides robust relative stability, an H/sub /spl infin//-norm disturbance attenuation and H/sub 2/ optimality. The H/sub /spl infin// norm of the transfer function from the external disturbance forces (e.g., earthquake, wind, and etc.) to the observed system states is restricted by a prescribed attenuation index /spl delta/. Preservation of robust H/sub 2/ optimality of uncertain structural systems is discussed. Considered uncertainties are both structured uncertainties and norm-bounded unstructured uncertainties. Numerical simulations that use the robust controller show significant reduction in vibrations. The resulting approach to robust control may be applied to analysis and design of practical structural systems.

Robust optimal pole-clustering in a vertical strip and disturbance rejection for uncertain Lagrange's systems

This paper presents an approach to design a state-feedback robust control law for uncertain Lagranges systems such that the designed closed-loop systems have the properties of robust pole-clustering within a vertical strip and disturbance rejection with anH∞-norm constraint. This approach is based on solving an algebraic Riccati equation with the adjustable scalars and prespecified parameters. The uncertainties considered include both unstructured and structured uncertainties in the system and the input matrices. Also, a constraint is established to verify that the proposed robust LQRs preserveH2 optimality with respect to a specific quadratic cost function.

A general theory for analysis and design of robust pole clustering in subregions of the complex plane

This paper presents a general theory for analysis and design of robust pole clustering in a very general subregion /spl Omega/ of the complex plane for uncertain systems with unstructured or structured uncertainties. The pole clustering regions of interest cover any /spl Omega/-transformable and non-/spl Omega/-transformable /spl Omega/-regions which are broader than those reported in the literature. Discussions regarding robust D-stability (robust pole clustering) and quadratic D-stability (quadratic pole clustering) are presented. Based on the Rayleigh principle, three new approaches are developed for analysis of robust pole clustering in a general subregion /spl Omega/ of the complex plane. By applying these analysis results, an output-feedback robust D-stability design method is developed for a general regional-pole placement of uncertain systems.

RC interconnect circuits and its balanced truncated models

Advance of high-speed deep-submicron VLSI technology requires chip interconnect and packaging to be modeled by distributed circuits. Such a detailed modeling level eventually results in large scale linear circuits to be analyzed. Here, even distributed RC interconnect models and their closed-forms are discussed and presented. The obvious advantage is to avoid difficulty of taking very large dimension matrix inverse that exists in previous conventional methods. Then, the balanced truncation method is applied to two even distributed RC interconnect cases by using these closed-forms of the models. The results show that extremely high order RC interconnect can be high-accurately approximated by only the third or higher order balanced model. When the source and load ports are included, the whole model may be approximated by the second or the first order balanced model. Simulations are executed in both time and frequency domains. The results may be applied to VLSI interconnect model reduction and design.

Robust control for structural systems with uncertainties

Natural hazards such as earthquakes and strong wind events place large forces on tall, slender structures and also on long bridges. The structural system usually can be described by a Lagrangian model. In view of numerous uncertainties due to model errors, stress calculations, material properties, and load environments, the system is uncertain. Here, the Lagrangian structural systems is modeled as an uncertain state space model. The paper develops a robust active control approach with uncertainties in the system, control input, and disturbance input matrices. Robust active control provides both robust stability and H(infinity ) disturbance attenuation. The H(infinity ) norm of the transfer function from the external disturbance forces to the observed system states is restricted by a prescribed attenuation index. Considered uncertainties are norm-bounded to robust control analysis and design of structural systems.

Robust Schur stability and eigenvectors of uncertain matrices

This paper presents the relationship between eigenvectors and Hurwitz stability of uncertain matrices. First, it reveals new necessary and sufficient conditions for stability of a nominal matrix A through the relationship of its eigenvectors and its symmetric criterion matrices. Three types of criterion matrices are adopted, i.e., the direct symmetric matrix A/sub s/=(A+A*)/2, the similarity transformed symmetric matrix and the Lyapunov-type symmetric matrix. Then, the necessary and sufficient conditions for robust stability of uncertain matrices are provided by using their eigenvector directions with respect to a basis constituted by their symmetric criterion matrix eigenvectors. The concerned uncertainties include both structured and unstructured uncertainties. The results may be applied to control systems for robust stability analysis and design.